volumetric pricing structure
EEP 162
Problem Set
Due May 1 1. Suppose that a water utility has a simple volumetric pricing structure and charges $800/af for water service – a price that just covers its average cost. Suppose that the utility’s marginal cost of service is $100/af and that consumers have a demand elasticity of -0.20. Baseline consumption is 1,000 af.
a) Calculate the average and marginal welfare cost of 10% and 20% rationing under the assumption that demand is linear. b) Repeat these calculations under the assumption that demand is isoelastic. c) Suppose the utility gives away the first 100 af of water to its customers. How would this affect your answer to a) and b)?
2. Consider a groundwater management problem where
Xt is the stock of groundwater at time t Yt is the quantity of groundwater extracted g(Yt) is the amount of recharge to the aquifer B(Yt) is the benefit of extracting Yt C(Xt,Yt) is the cost of pumping quantity Yt with a stock of Xt
In Mexico, there are property rights to groundwater but a large number of users. Groundwater used in agriculture is unregulated and hence subject to the problems of myopic behavior studied in class (i.e., a failure to consider user cost). Suppose that
g(Y ) = A +θY B(Y ) =αY1/2 C(X,Y ) = (γ −δ X)Y
(a) Determine the steady state levels of X and Y under myopic behavior. (b) Now suppose that the Mexican government subsidizes electricity usage by farmers, which is the main cost component of pumping groundwater. Thus, instead of producers paying C(X,Y), they only pay a fraction of actual extraction costs, with that fraction equal to φ , where 0 <φ < 1. Calculate the resulting levels of X and Y under myopic behavior. What is the effect of the subsidy on extraction and the stock levels. How do your answers to this part compare to the answers to part a)? Show your calculations, and make sure to give an intuitive explanation for the difference, if any.
3. Suppose there are two technologies that can be used for irrigation. Flood irrigation is relatively inefficient. For every 10 acre-feet of water applied to an acre of land, only 3 are used by the plants. Drip irrigation is much more efficient; if 4 acre-feet of water is applied to the land, plants will actually consume 3 acre-feet. The production function is given by
y = 4e – 0.25e2
where e denotes the amount of water actually consumed by the plants and y the output per acre. All land has identical quality. The price of water is $1 per acre-foot and the price of output is $2 per unit of output. Drip irrigation has a capital cost of $3 per acre, while flood irrigation has a capital cost of $1 per acre.
a) Derive the optimal applied water use for each of the two technologies. b) Identify which technology will be chosen. Explain your answer. c) Discuss how your answer would change if the effectiveness of drip and flood irrigation depended on land quality. Your answer should indicate both the likely outcome and the reason it occurs.
